The aim of this workshop is to encourage academic activities in the area of geometric topology in Korea and promote friendly relations between researchers in this area. This year we focus on knot theory and low-dimensional manifolds. We hope this workshop contributes to acceleration of research in this field.
|July 31||Room 4416 Natural Science Building, KAIST, Daejeon|
|PM 03:00-04:20||Kent E. Orr||TBA|
|PM 04:40-06:00||Yuanan Diao||Topological and geometrical problems of Random knots|
|August 2||Busan Youth Hostel Arpina, Heaundea-gu, Busan|
|09:30-10:10||Kent E. Orr||TBA|
|10:20-11:00||Yuanan Diao||Some geometric problems of physical knots I|
|11:10-11:50||Sang Jin Lee||Conjugacy classes in Garside groups|
|11:50-01:30||--- Lunch ---|
|01:30-02:10||Kent E. Orr||TBA|
|02:20-03:00||Yuanan Diao||Some geometric problems of physical knots II|
|03:00-03:30||--- Coffee Break ---|
|03:30-04:10||Jae Choon Cha||L^2 signatures and minimal genus in 4-manifolds|
|Participants accompanied with family||220,000|
|Participants not accompanied with family||75,000|
Very limited funding may be available to those not supported by other grants. Please contact the organizers (see the contact information below).
We have reserved a block of rooms for participants. We welcome your family; for more comfortable stay, we will assign to each family a guest house with a bedroom and bathroom. Participants not accompanied with family will be asked to share similar guest houses.
For any inquiries on the workshop, please contact:
Korea Advanced Institute of Science and Technology
373-1 Guseong-dong, Yuseong-gu, Daejeon 305-701, Korea
For more information on the hotel, please see the home page of Busan Youth Hostel Arpina (in Korean)
In this talk, I will give an overview of the various topological and geometrical problems encountered in random knots. I will briefly discuss several commonly used random knot models, state the problems and present some theoretical as well as numerical results. At the end, I will discuss the random knotting and linking problem in a confined space.
In this talk, I will mainly address some geometric problems associated with the ropelength of a physical knot, that is, a knot realized with a rope of certain thickness. In particular, I will discuss the global ropelength lower bound for any non-trivial knot, the general ropelength lower bound for a non-trivial knot in terms of its crossing number, and the general ropelength upper bound for a non-trivial knot in terms of its crossing number.
In this talk, I will continue the topics discussed in the first part. I will discuss several approaches aimed to improve the general ropelength upper bound of a knot and present some results. Some numerical results about the ropelength of physical knots will also be presented. At the end, I will discuss some recent results regarding the total curvature of physical knots.
The Garside group is a lattice-theoretic generalization of braid groups and Artin groups of finite type. We will talk about the notion of Garside groups and the structure of conjugacy classes, and discuss the asymptotic behavior of infimum under taking power and the applications of this results. If time allowed, some related results will also be discussed.